Kitap 13
28
represented existing things as composed of that which is smallest.)Perhaps the Atomists; but cf. Aristot. Met. 1.8.3, 4. We get, then, that the unit is the material element of numbers, and at the same time is prior to the number 2; and again we get that it is posterior to 2 regarded as a whole or unity or form. On the other hand, through looking for the universal, they were led to speak of the unity predicated of a given number as a part in the formal sense also. But these two characteristics cannot belong simultaneously to the same thing.
29
And if Unity itself must only be without positionIf the text is sound (and no convincing emendation has been suggested), it seems best to understand ἄθετον in a rather wider sense than the semi-technical one put forward by Ross. Without position = not localized, i.e. abstract. Unity as a principle has no concrete instance.(for it differs only in that it is a principle) and 2 is divisible whereas the unit is not, the unit will be more nearly akin to Unity itself; and if this is so, Unity itself will also be more nearly akin to the unit than to 2. Hence each of the units in 2 will be prior to 2. But this they deny; at least they make out that 2 is generated first.Cf. Aristot. Met. 13.7.5. Further, if 2 itself and 3 itself are each one thing, both together make 2. From what, then, does this 2 come?
1
Since there is no contact in numbers, but units which have nothing between them—e.g. those in 2 or 3—are successive, the question might be raised whether or not they are successive to Unity itself, and whether of the numbers which succeed it 2 or one of the units in 2 is prior.
2
We find similar difficulties in the case of the genera posterior to numberCf. Aristot. Met. 13.6.10.—the line, plane and solid. Some derive these from the species of the Great and Small; viz. lines from the Long and Short, planes from the Broad and Narrow, and solids from the Deep and Shallow. These are species of the Great and Small.
